In recent years, thin-film transistors having a semiconductor layer formed of an oxide semiconductor material, and semiconductor devices and display devices including such thin-film transistors, have been under intense development. In comparison with a transistor having a conventional semiconductor layer of amorphous silicon, a thin-film transistor having a semiconductor layer of an oxide semiconductor material achieves markedly increased mobility and rapid drive performance. This is an important contribution to display devices having high definition and large displays. The most common way to refer to an oxide semiconductor material formed in an amorphous state is a transparent amorphous oxide semiconductor (TAOS) material.